(a) Explanation Given information: The table given below shows the population of Florida in several years: Population of Florida Year Population(in thousands) 2000 16,047 2002 16,341 2004 17,314 2006 18,019 2008 18,328 2009 18,538 Graph: To graph the points on scatter plot, follow the steps using graphing calculator. First press the 2 nd key and then Y = and make sure that Plot 1 is ON and choose the scatter plot icon in type. Go to Y 1 and then press the key STAT and then in edit enter the data in L 1 and L 2 . Now, press the ZOOM 9 key and TRACE key to produce the scatter plot of given function in standard window as shown below. Figure (1) Interpretation: From the scatter plot of give data of population it can be observed that the population of Florida is increasing every year. (b) To determine To find: The slope of the secant line P Q i for i = 1 , 2 , 3 . Answer The slopes of the secant line P Q i for i = 1 , 2 , 3 are 313.86, 244.8 and 210 respectively. Explanation Given information: The table given below shows the population of Florida in several years: Population of Florida Year Population(in thousands) 2000 16,047 2002 16,341 2004 17,314 2006 18,019 2008 18,328 2009 18,538 The point P represents the points corresponding to 2009, Q 1 the point corresponding to 2002, Q 2 the point corresponding to 2004 and Q 3 the point corresponding to 2008. Calculation: Simplify the slope of the secant line P Q 1 . m = y 2 − y 1 x 2 − x 1 = 16341 − 18538 2002 − 2009 = − 2197 − 7 = 313.86 So, the slope of the secant line P Q 1 is equal to 313.86. Simplify the slope of the secant line P Q 2 . m = y 2 − y 1 x 2 − x 1 = 17314 − 18538 2004 − 2009 = − 1224 − 5 = 244.8 So, the slope of the secant line P Q 2 is equal to 244.8. Simplify the slope of the secant line P Q 3 . m = y 2 − y 1 x 2 − x 1 = 18328 − 18538 2008 − 2009 = − 210 − 1 = 210 So, the slope of the secant line P Q 3 is equal to 210. Therefore, the slopes of the secant line P Q i for i = 1 , 2 , 3 are 313.86, 244.8 and 210 respectively. (c) To determine To find: The average rates of change from Q i to P . Answer The average rate of change in the population of the given data is 244,800. Explanation Given information: The table given below shows the population of Florida in several years: Population of Florida Year Population(in thousands) 2000 16,047 2002 16,341 2004 17,314 2006 18,019 2008 18,328 2009 18,538 The point P represents the points corresponding to 2009, Q 1 the point corresponding to 2002, Q 2 the point corresponding to 2004 and Q 3 the point corresponding to 2008. Calculation: The slopes of the secant line P Q i for i = 1 , 2 , 3 are 313.86, 244.8 and 210 respectively. The average rate of change in the population of the given data is 244,800. Therefore, the average rate of change in the population of the given data is 244,800. (d) To determine To find: The instantaneous rate of change of population on July 1, 2009. Answer The instantaneous rate of change of population on July 1, 2009 is 210,000. Explanation Given information: The table given below shows the population of Florida in several years: Population of Florida Year Population(in thousands) 2000 16,047 2002 16,341 2004 17,314 2006 18,019 2008 18,328 2009 18,538 Calculation: The slope of the secant line from year 2009 to 2000 is 210. The average rate of change in the population of the given data is 210,000. Therefore, the instantaneous rate of change of population on July 1, 2009 is 210,000. (e) To determine To find: The estimated population of Florida in 2020. Answer The estimated population of Florida in 2020 is 442738. Explanation Given information: The table given below shows the population of Florida in several years: Population of Florida Year Population(in thousands) 2000 16,047 2002 16,341 2004 17,314 2006 18,019 2008 18,328 2009 18,538 Calculation: Consider that the population growth is liner function. The formula for a linear equation in slope-intercept form is: y = m x + c The required equation is: y = 210 x + 18538 Substitute 2020 for x in the above equation to find the population in 2020, y = 210 ( 2020 ) + 18538 = 442738 Therefore, the estimated population of Florida in 2020 is 442738.

Calculus: Graphical, Numerical, Algebraic: Solutions Manual

3rd Edition

ISBN: 9780132014144

Author: Ross L. Finney, Franklin Demana, Bert K. Waits, Daniel Kennedy

Publisher: Pearson Prentice Hall

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Question

Chapter 2, Problem 51RE

(a)

To determine

To graph: A scatter plot of the given data.

(a)

Expert Solution

Explanation of Solution

Given information:

The table given below shows the population of Florida in several years:

Population of Florida
Year	Population(in thousands)
2000	16,047
2002	16,341
2004	17,314
2006	18,019
2008	18,328
2009	18,538

Graph:

To graph the points on scatter plot, follow the steps using graphing calculator.

First press the 2nd key and then Y= and make sure that Plot 1 is ON and choose the scatter plot icon in type.

Go to Y1 and then press the key STAT and then in edit enter the data in L1 and L2 .

Now, press the ZOOM9 key and TRACE key to produce the scatter plot of given function in standard window as shown below.

Calculus: Graphical, Numerical, Algebraic: Solutions Manual, Chapter 2, Problem 51RE

Figure (1)

Interpretation: From the scatter plot of give data of population it can be observed that the population of Florida is increasing every year.

(b)

To determine

To find: The slope of the secant line PQi for i=1,2,3 .

(b)

Expert Solution

Answer to Problem 51RE

The slopes of the secant line PQi for i=1,2,3 are 313.86, 244.8 and 210 respectively.

Explanation of Solution

Given information:

The table given below shows the population of Florida in several years:

Population of Florida
Year	Population(in thousands)
2000	16,047
2002	16,341
2004	17,314
2006	18,019
2008	18,328
2009	18,538

The point P represents the points corresponding to 2009, Q1 the point corresponding to 2002, Q2 the point corresponding to 2004 and Q3 the point corresponding to 2008.

Calculation:

Simplify the slope of the secant line PQ1 .

m=y2−y1x2−x1=16341−185382002−2009=−2197−7=313.86

So, the slope of the secant line PQ1 is equal to 313.86.

Simplify the slope of the secant line PQ2 .

m=y2−y1x2−x1=17314−185382004−2009=−1224−5=244.8

So, the slope of the secant line PQ2 is equal to 244.8.

Simplify the slope of the secant line PQ3 .

m=y2−y1x2−x1=18328−185382008−2009=−210−1=210

So, the slope of the secant line PQ3 is equal to 210.

Therefore, the slopes of the secant line PQi for i=1,2,3 are 313.86, 244.8 and 210 respectively.

(c)

To determine

To find: The average rates of change from Qi to P .

(c)

Expert Solution

Answer to Problem 51RE

The average rate of change in the population of the given data is 244,800.

Explanation of Solution

Given information:

The table given below shows the population of Florida in several years:

Population of Florida
Year	Population(in thousands)
2000	16,047
2002	16,341
2004	17,314
2006	18,019
2008	18,328
2009	18,538

The point P represents the points corresponding to 2009, Q1 the point corresponding to 2002, Q2 the point corresponding to 2004 and Q3 the point corresponding to 2008.

Calculation:

The slopes of the secant line PQi for i=1,2,3 are 313.86, 244.8 and 210 respectively. The average rate of change in the population of the given data is 244,800.

Therefore, the average rate of change in the population of the given data is 244,800.

(d)

To determine

To find: The instantaneous rate of change of population on July 1, 2009.

(d)

Expert Solution

Answer to Problem 51RE

The instantaneous rate of change of population on July 1, 2009 is 210,000.

Explanation of Solution

Given information:

The table given below shows the population of Florida in several years:

Population of Florida
Year	Population(in thousands)
2000	16,047
2002	16,341
2004	17,314
2006	18,019
2008	18,328
2009	18,538

Calculation:

The slope of the secant line from year 2009 to 2000 is 210. The average rate of change in the population of the given data is 210,000.

Therefore, the instantaneous rate of change of population on July 1, 2009 is 210,000.

(e)

To determine

To find: The estimated population of Florida in 2020.

(e)

Expert Solution

Answer to Problem 51RE

The estimated population of Florida in 2020 is 442738.

Explanation of Solution

Given information:

The table given below shows the population of Florida in several years:

Population of Florida
Year	Population(in thousands)
2000	16,047
2002	16,341
2004	17,314
2006	18,019
2008	18,328
2009	18,538

Calculation:

Consider that the population growth is liner function. The formula for a linear equation in slope-intercept form is:

y=mx+c

The required equation is:

y=210x+18538

Substitute 2020 for x in the above equation to find the population in 2020,

y=210(2020)+18538=442738

Therefore, the estimated population of Florida in 2020 is 442738.

Chapter 2, Problem 50RE

Chapter 2, Problem 52RE

Chapter 2 Solutions

Calculus: Graphical, Numerical, Algebraic: Solutions Manual

Ch. 2.1 - Prob. 1QR Ch. 2.1 - Prob. 2QR Ch. 2.1 - Prob. 3QR Ch. 2.1 - Prob. 4QR Ch. 2.1 - Prob. 5QR Ch. 2.1 - Prob. 6QR Ch. 2.1 - Prob. 7QR Ch. 2.1 - Prob. 8QR Ch. 2.1 - Prob. 9QR Ch. 2.1 - Prob. 10QR

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